Dirichlet character χ3360(83,⋅)\chi_{3360}(83,\cdot)

• Label: 3360.83
• Modulus: $3360$
• Conductor: $3360$
• Order: $8$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$3360$
Conductor:	$3360$
Order:	$8$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 3360.ew

$\chi_{3360}(83,\cdot)$ $\chi_{3360}(587,\cdot)$ $\chi_{3360}(1763,\cdot)$ $\chi_{3360}(2267,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{8})$
Fixed field:	8.8.6525699489792000000.1

Values on generators

$(1471,421,1121,2017,1921)$ → $(-1,e\left(\frac{7}{8}\right),-1,-i,-1)$

First values

$a$	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 3360 }(83, a)$	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{1}{8}\right)$